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The Approximation Ratio for Boolean Max-k-CSP

Algorithms & optimization · partial

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Statement

How well can an arbitrary boolean constraint satisfaction problem of arity kk be approximated in polynomial time? The paper gives a (k/2k)(k/2^k)-approximation, improving the previous best constant of 0.626612 k/2k0.626612\,k/2^k due to Makarychev and Makarychev.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Ainesh Bakshi, using GPT-5.6 Sol Max

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    "GPT 5.6 Sol Max assisted in the lengthy computations that appear in the proof." Computational support inside a human-led argument.

    Removes the constant factor from the previous best guarantee; whether k/2kk/2^k is optimal is not settled here.

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